Uncertainty and sensitivity analysis of functional risk curves based on Gaussian processes

Highlights: • The Gaussian process metamodel allows to build a functional risk curve (FRC) with a limited number of computer model runs. • Two sensitivity analysis methods are developed for the functional risk curve as quantity of interest. • Sensitivity analysis can be realized via the aggregated Sobol' indices . • The Perturbed-Law based sensitivity Indices (PLI) give the effect of change of input pdf on the FRC. • An example from the non-destructive control domain illustrates all the proposed methods. -- Abstract: A functional risk curve gives the probability of an undesirable event as a function of the value of a critical parameter of a considered physical system. In several applicative situations, this curve is built using phenomenological numerical models which simulate complex physical phenomena. To avoid cpu-time expensive numerical models, we propose to use Gaussian process regression to build functional risk curves. An algorithm is given to provide confidence bounds due to this approximation. Two methods of global sensitivity analysis of the model random input parameters on the functional risk curve are also studied. In particular, the PLI sensitivity indices allow to understand the effect of misjudgment on the input parameters' probability density functions.